May be it caused by one of your extensions or plug-ins. Try to manually disable them all and close (exit) all other internet related apps and try again to change your homepage. Does this work?

Also it maybe caused by a threat or badware application. Try making a full scan whith an updated Internet security program (i.e. Kaspersky internet security, Norton Internet security & ...) and try to change your homepage after restarting your system.

Have your problem solved???

May be it caused by one of your '''extensions or plug-ins'''. Try to '''manually disable''' them all and '''close (exit) all other internet related apps''' and try again to change your homepage. Does this work?
Also it maybe caused by a '''threat or badware application'''. Try making a full scan whith an updated Internet security program (i.e. Kaspersky internet security, Norton Internet security & ...) and try to change your homepage after restarting your system.
Have your problem solved???

If you do not keep changes after a restart then see:
*http://kb.mozillazine.org/Preferences_not_saved
*https://support.mozilla.org/kb/Preferences+are+not+saved
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Which security software (firewall, anti-virus) do you have?